A method to assess the robustness of complex mathematical models used for quantitative interpretation of experimental data by nonlinear regression analysis: application to high-affinity binding models

Abstract

Nonlinear regression is widely used to fit experimental data to a specific mathematical model to extract numerical values for parameters representing the studied process. However, assessing the degree of precision that can be expected from such an analysis for a given parameter can be quite challenging for complex mathematical models. To address this issue, we propose here a method based on the analysis of a large number of data sets generated in such a way to mimic specific experimental conditions. Applying this methodology to high-affinity binding models, we report here a quantitative analysis of the robustness of such models, and how the precision on the fitting parameters can be expected to vary based on, e.g., the initial experimental conditions, the number or distribution of experimental points, or the experimental variability. We also show that these models, although widely used, are intrinsically limited by the fact that the two main fitting parameters, one representing the concentration of the studied species and the other its affinity, are inversely correlated, but demonstrate that this limitation can be overcome by global analysis of multiple data series generated at different concentrations of the titrated species.